Track quality is a major factor in railroad safety. One accepted indicator of track quality is the rail's vertical track modulus. Track modulus is defined as the coefficient of proportionality between the vertical rail deflection and the vertical contact pressure between the rail base and track foundation; it can be re-stated as the supporting force per unit length of rail, per unit rail deflection.
Railway track has several components that all contribute to track stiffness including the rail, subgrade, ballast, subballast, ties, and fasteners. The rail directly supports the train wheels and is supported on a rail pad and held in place with fasteners to crossties. The crossties rest on a layer of rock ballast and subballast used to provide drainage. The soil below the subballast is the subgrade.
The subgrade resilient modulus and subgrade thickness have the strongest influence on track modulus. These parameters depend upon the physical state of the soil, the stress state of the soil, and the soil type. Track modulus increases with increasing subgrade resilient modulus, and decreases with increasing subgrade layer thickness. Ballast layer thickness and fastener stiffness are the next most important factors. Increasing the thickness of the ballast layer and or increasing fastener stiffness will increase track modulus. This effect is caused by the load being spread over a larger area. It is desirable to measure the net effective track modulus, which includes all these factors.
Track modulus is important because it affects track performance and maintenance requirements. Both low track modulus and large variations in track modulus are undesirable. Low track modulus has been shown to cause differential settlement that then increases maintenance needs. Large variations in track modulus, such as those often found near bridges and crossings, have been shown to increase dynamic loading, which reduces the life of the track components resulting in shorter maintenance cycles. It is known that reducing variations in track modulus at grade (i.e. road) crossings leads to better track performance and less track maintenance. Ride quality, as indicated by vertical acceleration, is also strongly dependent on track modulus.
The economic constraints of both passenger and freight rail service are moving the industry to higher-speed rail vehicles and the performance of high-speed trains are likewise strongly dependent on track modulus. At high speeds, there is an increase in track deflection caused by larger dynamic forces. These forces become significant as rail vehicles reach 50 km/hr (30 mph) and rail deflections increase with higher vehicle speeds up to a critical speed. It is suggested that track with a high and consistent modulus will allow for higher train speeds and therefore increased performance and revenue.
Previous localized field-testing has shown that it is possible to measure areas of low-track modulus, variable-track modulus, void deflection, variable total deflection, and inconsistent rail deflection. In the past, these known systems have been used to identify sections of track with poor performance. Although these measurements are useful; they are expensive and only are made over short distances (˜tens of meters). The ability to make these measurements continuously over large sections of track is desirable.
Previous vertical track modulus measurement systems can be placed in two categories: 1) trackside measurements, and 2) on-board measurements. With the trackside approach, a section of track is closed to rail traffic and a work crew uses specialized equipment to make measurements at various discrete locations.
In all trackside methods, rail deflection is measured before and after a static “point” load is applied. Differences lie in the number of deflection measurements made and how those measurements are used to estimate track modulus. Common trackside approaches include the Beam on Elastic Foundation method and the Deflection Basin method.
The Beam on an Elastic Foundation method uses a structural model, known as the Winkler Model, to represent the track system. The Winkler model represents a point load applied to an infinite Bernoulli beam on an infinite elastic foundation Trackside measurements of the deflection at the point where the load is applied are taken for a known load and modulus can then be calculated using:
                    u        =                              1            4                    ⁢                                    (                              1                                  E                  ⁢                                                                          ⁢                  1                                            )                                      1              3                                ⁢                                    (                              P                                  w                  0                                            )                                      4              3                                                          (        1        )            where:                u is the track modulus        E is the modulus of elasticity of the rail        I is the moment of inertia of the rail        P is the load applied to the track        w0 is the deflection of the rail at the loading pointThis method only requires a single measurement and it has been suggested to be the best method for field measurement of track modulus. Its major limitation is that it provides only information for a single point along the rail. In reality, the modulus may be very different only a meter away. Also, if multiple loads are present. as with multi-axle railway vehicles used to apply the point load, small deflections must be assumed and superposition is needed. In this case the Winkler model cannot be simplified as in Equation (1) and an iterative solution is required. Also, slack in the rail can cause non-linearity in the load/deflection relationship. Therefore, a small load should be applied to determine the zero displacement position for the measurement. A heavy load is then applied and used as the loaded measurement. This further complicates this technique.        
The second trackside technique, the Deflection Basin Method, uses the vertical equilibrium of the loaded rail to determine track modulus. In this approach rail deflection caused by a point load(s) is measured at several (ideally infinite) locations along the rail and the entire deflected “area” calculated. Using a force balance this deflected area, or deflection basin, can be shown to be proportional to the integral of the rail deflection:
                    P        =                                            ∫                              -                ∞                            ∞                        ⁢                                          q                ⁡                                  (                  x                  )                                            ⁢                                                          ⁢                              ⅆ                x                                              =                                                    ∫                                  -                  ∞                                ∞                            ⁢                              u                ⁢                                                                  ⁢                                  δ                  ⁡                                      (                    x                    )                                                  ⁢                                                                  ⁢                                  ⅆ                  x                                                      =                          u              ⁢                                                          ⁢                              A                δ                                                                        (        2        )            where:                P is the load on the track        q(x) is the vertical supporting force per unit length        u is the track modulus        δ(x) is the vertical rail deflection        Aδ is the deflection basin area (area between the original and deflected rail positions)        x is the longitudinal distance along the trackThe multiple deflection measurements required for this method result in longer traffic delays. Once again, both heavy and light loads are used to eliminate slack, which further increase the delays.        
Both of these methods are time consuming and expensive and all suffer from the major limitation that the measured modulus is only valid along a small length of track. It is desirable to have a moving, i.e., on-board, modulus measurement system.
On-board measurements are made from a moving railcar and are more desirable because they can be made with less interruption of rail traffic and over longer distances. On-board measurements, however, are difficult because there is no stable reference frame. And, present on-board systems are labor intensive and move at slow speeds. Thus, they are limited to short distances (e.g. hundreds of meters) and still interrupt traffic. These previous systems use a long rigid truss that rides on two unloaded wheels. This truss creates a straight line, or cord, that is used as a reference for the measurement. A third wheel is then used to apply a load at midpoint of the cord (or truss) and the relative displacement between the loaded wheel and the unloaded truss is measured. The truss must be long enough, generally 30.48 m (100 ft), so that the two endpoints are not affected by the load at the center of the truss. This method again requires two measurements one with a light load, made with a similar truss, and the heavy load, to distinguish between changes in geometry and changes in modulus. The output of this approach is a measurement of the relative displacement of the loaded wheel with respect to the unloaded wheel and from this measurement the track modulus is then estimated.
One vehicle, called the Track Loading Vehicle (TLV), uses this approach. This vehicle is capable of measuring track modulus at speeds of 16.1 km/hr (10 mph). The TLV uses two cars, each with a center load bogie capable of applying loads from 4.45 kN to 267 kN (1 to 60 kips). A light load (13.3 kN or 3 kips) is applied by the first vehicle while a heavier load is applied by the second vehicle. A laser-based system on each vehicle measures the deflections of the rail caused by the center load bogies. The test procedure involves two passes over a section of track-first applying a 44.5 kN (10 kip) load and then a 178 kN (40 kip) load. The TLV still has limitations. First, tests are often performed at speeds below 16.1 km/hr (10 mph) so it is difficult to test long section of track (hundreds of miles). Second, significant expense in both equipment and personnel are required for operation. For these reasons the TLV has not yet been widely implemented.
Thus it is desirable to have an apparatus and method to determine track modulus from a moving railcar that is inexpensive, does not require significant support equipment, operates at higher speeds and could potentially be automated.